Medium effects on pion production in heavy ion collisions

Abstract

Within the framework of the relativistic Vlasov--Uehling--Uhlenbeck transport model based on the relativistic nonlinear $\mathrm{NL}\ensuremath{\rho}$ interaction, we study pion in-medium effects on the ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio in $\text{Au}+\text{Au}$ collisions at the energy of $E/A=400\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$. These effects include the isospin-dependent pion $s$-wave and $p$-wave potentials, which are taken from calculations based on the chiral perturbation theory and the $\mathrm{\ensuremath{\Delta}}$-hole model, respectively. We find that the ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio in this collision is suppressed by the pion $s$-wave potential but enhanced by the $p$-wave potential, with a net effect of a significantly suppressed ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio. Including also the in-medium threshold effects on $\mathrm{\ensuremath{\Delta}}$ resonance production and decay and using a nuclear symmetry energy with a slope parameter $L=59\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$ by reducing the coupling of isovector-vector $\ensuremath{\rho}$ meson to nucleon, our result is in good agreement with measured ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio from the FOPI Collaboration. We further investigate the pion in-medium effects on the ratio of charged pions as a function of their kinetic energies.